Control of space charge redistribution to correct aberrations in charged particle beams

The charged particle beam in confining fields tends to an equilibrium configuration. The process, as well known, entails space charge redistribution and nonlinear aberrations. In most cases the beam phase distribution oscillates about equilibrium one due to excess of energy. Appropriate choice of the confining fields allows controlling frequency and amplitude of the oscillation that beam aberrations remain reversible and exhibit at the exit a required phase, for example, close to the initial phase when the aberrations are small. Beam optics with corrected aberrations may be designed on the principle. An example of the optics for matching beam into a radio-frequency-quadruple accelerator (RFQ) is presented.